The incident occurred after Thomas missed a par putt during the Sentry Tournament of Champions’ third round in Hawaii.
“I’m an adult. I’m a grown man. There’s absolutely no reason for me to say anything like that.
“It’s terrible. I’m extremely embarrassed. It’s not the kind of person that I am … But unfortunately I did it and I have to own up to it and I’m very apologetic.
“I deeply apologize to everybody and anybody who I offended and I’ll be better because of it,” added Thomas.
“As he expressed after his round, we agree that Justin’s comment was unacceptable,” the PGA Tour said in a statement according to the AFP news agency, which added Thomas is likely to be fined for conduct “unbecoming of a professional.”
“There is no place for it in sports. We must continue to work for greater inclusion and acceptance,” tweeted David. “That’s how we all ultimately will win.”
Going into Sunday’s final round Thomas is tied for fifth place, four shots behind co-leaders Harris English and Ryan Palmer.